Solving Rocket Launch Equations in matlab

In summary: Please provide more detailed information about your attempts to solve the problem using the given equations and the issues you encountered.In summary, the conversation discusses the use of a Super Loki rocket to launch a small payload to above 100 km altitude in a sub orbital flight. The apogee is to be found using both numerical and analytic techniques, with specifications given for payload mass, thrust, launch mass, burn time, and solid fuel specific impulse. The question also addresses which differential equation to use for solving the problem and the difficulties encountered when using ode45 to solve the equation dvdt = -F/M.
  • #1
mysticboon
3
0

Homework Statement


A Super Loki rocket (http://en.wikipedia.org/wiki/Loki_(rocket )) is used to launch a small
payload to above 100 km altitude in a sub orbital flight. Ignoring atmospheric resistance, find the
apogee using both numerical and analytic techniques (solve the differential equations given in
the lecture notes). Use the specifications given below.
Payload mass (unpowered 2ndstage)
6 kg
Thrust (constant until burnout–kilo-Newtons)
18 kNt
Launch (take-off) mass
29 kg
Burntime
2.1 sec
HTBP solid fuel specific impulse
238 sec
At the end of the 2.1 sec burn, the payload is explosive bolt“ launched” to coast to apogee. This
does NOT effect the calculations.




Homework Equations


Basically my question is what differential equation am I to use to solve this? I'm using the equations give here
http://exploration.grc.nasa.gov/education/rocket/rktpow.html
I solved the problem analytically already so I have a general idea what the answer should look like.



The Attempt at a Solution


I attempted to use ode45 to solve the equation dvdt = -F/M but the ode solver gets an error with the time step I'm using.
 
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  • #2
Are we supposed to guess what you did? You still must show specific work, rather than say, "I did this. It didn't work. What went wrong?"
 

Related to Solving Rocket Launch Equations in matlab

1. How do I set up the initial conditions for a rocket launch in matlab?

To set up the initial conditions for a rocket launch in matlab, you will need to define variables such as the initial velocity, initial height, and initial acceleration of the rocket. These variables will depend on the specific scenario you are trying to model. You can use the input function in matlab to prompt the user for these initial conditions, or you can manually assign values to these variables.

2. What equations do I need to use to model a rocket launch in matlab?

To model a rocket launch in matlab, you will need to use the equations of motion, specifically the kinematic equations. These equations describe the relationship between an object's position, velocity, and acceleration. In particular, you will need to use the equations for constant acceleration, as rocket launches typically involve a constant acceleration due to the force of the rocket's engines.

3. How do I plot the trajectory of a rocket launch in matlab?

To plot the trajectory of a rocket launch in matlab, you will need to use the plot function. This function takes in two arrays, one for the x-coordinates and one for the y-coordinates, and plots the corresponding points on a graph. You will need to calculate the x and y positions of the rocket at regular intervals using the equations of motion, and then use these values to create the arrays for the plot function.

4. Can I use matlab to simulate different scenarios for a rocket launch?

Yes, matlab can be used to simulate different scenarios for a rocket launch. By changing the initial conditions, such as the initial velocity or height, you can model different launch scenarios and observe how they affect the trajectory of the rocket. This can be useful in analyzing the performance of different rocket designs or predicting the outcome of a launch with varying conditions.

5. How accurate are the results from solving rocket launch equations in matlab?

The accuracy of the results from solving rocket launch equations in matlab will depend on the accuracy of the initial conditions and the equations used. If the initial conditions are based on real-world data and the equations are applied correctly, the results should be fairly accurate. However, it is important to note that there are many factors that can affect the trajectory of a rocket launch, such as air resistance and wind, which may not be accounted for in a simple matlab simulation.

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